English

On the quaternionic short-time Fourier and Segal-Bargmann transforms

Complex Variables 2020-09-02 v1

Abstract

In this paper, we study a special one dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal-Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb's uncertainty principle. We provide also the reproducing kernel associated to the Gabor space considered in this setting.

Cite

@article{arxiv.2009.00073,
  title  = {On the quaternionic short-time Fourier and Segal-Bargmann transforms},
  author = {Antonino De Martino and Kamal Diki},
  journal= {arXiv preprint arXiv:2009.00073},
  year   = {2020}
}

Comments

to appear in Mediterranean Journal of Mathematics

R2 v1 2026-06-23T18:13:22.605Z